We would like to study a weakly coupled system of semi-linear classical damped wave equations with moduli of continuity in nonlinearities whose powers belong to the critical curve in the $p-q$ plane. The main goal of this paper is to find out sharp conditions of these moduli of continuity which classify between global (in time) existence of small data solutions and finite time blow-up of (even) small data solutions.

中文翻译：

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半线性阻尼波动方程弱耦合系统中非线性临界规律的相互作用

我们想研究具有非线性连续模的半线性经典阻尼波动方程的弱耦合系统，其幂属于临界曲线 $磷-q$飞机。本文的主要目标是找出这些连续性模的尖锐条件，将小数据解决方案的全局（及时）存在和（偶数）小数据解决方案的有限时间爆炸分类。